Although the publicity suggests that it's a strict hierarchy - horse riders give way to cyclists - the new rules H1 etc. do not actually say that. They give specific cases, eg

- horse riders should give way to cyclists on a 'parallel' crossing - obviously
- cyclists should give way to horse riders on a bridleway - sensible

An actual hierarchy - as quoted in the OP - is not in the Code. Perhaps it was invented to get the changes noticed.